On Typical Compact Convex Sets in Hilbert Spaces

De Blasi, F.

Displaying similar documents to “On Typical Compact Convex Sets in Hilbert Spaces”

Some geometric properties of typical compact convex sets in Hilbert spaces

F. de Blasi (1999)

Studia Mathematica

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An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection $q_{X} (e)$ from e to X has fixed cardinality n+1 ( $n \subseteq ℕ$ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection $p_{X} (e)$ from e to X where X is a compact subset of .

Properties of typical bounded closed convex sets in Hilbert space.

de Blasi, F.S., Zhivkov, N.V. (2005)

Abstract and Applied Analysis

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On total differential inclusions

Alberto Bressan, Fabián Flores (1994)

Rendiconti del Seminario Matematico della Università di Padova

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Generic well-posedness in some classes of optimization problems

Julian Petrov Revalski (1987)

Acta Universitatis Carolinae. Mathematica et Physica

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Ambiguous loci of the farthest distance mapping from compact convex sets

F. De Blasi, J. Myjak (1995)

Studia Mathematica

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Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by $K^{0}$ the set of all X ∈ K() such that the farthest distance mapping $a \mapsto M_{X} (a)$ is multivalued on a dense subset of . It is proved that $K^{0}$ is a residual dense subset of K().

A class of locally convex spaces without $𝒞$ -webs

Manuel Valdivia (1982)

Annales de l'institut Fourier

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In this article we give some properties of the tensor product, with the $ϵ$ and $π$ topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.

A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets

Ivanov, M., Zlateva, N. (2000)

Serdica Mathematical Journal

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We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.

Some fixed point theorems

Barada Ray (1976)

Fundamenta Mathematicae

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